Control Variate Multifidelity Estimators for the Variance and Sensitivity Analysis of Mesostructure–Structure Systems

Abstract

Variance and sensitivity analysis are challenging tasks when the evaluation of system performances incurs a high-computational cost. To resolve this issue, this paper investigates several multifidelity statistical estimators for the responses of complex systems, especially the mesostructure–structure system manufactured by additive manufacturing. First, this paper reviews an established control variate multifidelity estimator, which leverages the output of an inexpensive, low-fidelity model and the correlation between the high-fidelity model and the low-fidelity model to predict the statistics of the system responses. Second, we investigate several variants of the original estimator and propose a new formulation of the control variate estimator. All these estimators and the associated sensitivity analysis approaches are compared on two engineering examples of mesostructure–structure system analysis. A multifidelity metamodel-based sensitivity analysis approach is also included in the comparative study. The proposed estimator demonstrates its strength in predicting variance when only a limited number of expensive high-fidelity data are available. Finally, the pros and cons of each estimator are discussed, and recommendations are made on the selection of multifidelity estimators for variance and sensitivity analysis.